How Do You Construct a Triangle of Forces?

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Homework Help Overview

The discussion centers around the concept of a "triangle of forces," specifically how to construct it using given force vectors and their angles. Participants are examining the relationships between the forces and their representations in a diagram.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants are discussing the angles associated with the force vectors and how they relate to the triangle's construction. There are attempts to clarify the positioning of the vectors and their angles with respect to the horizontal and vertical axes.

Discussion Status

Some participants have provided insights into the angles and positioning of the vectors, suggesting a clearer understanding of the triangle's formation. There is an acknowledgment of the concept of "free vectors," indicating a productive exploration of the topic.

Contextual Notes

Participants are working with specific angles and forces as described in a textbook, and there may be assumptions regarding the definitions and properties of vectors that are being discussed.

riddle
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What's a "triangle of forces" (triforce, lol)

I've attached a snip from my textbook. I don't get how they make that triangle, and how they get those angles. Can someone please help.
 

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The "7 N" force is set to be vertical since it is the gravitational force on an object.
The "A, B, P" diagram shows that vector T_A is at 30 degrees to the horizontal and so is at 90- 30= 60 degrees to the vertical. That's where they get the angle at the bottom of the triangle. The vector T_B is at 40 degrees to the horizontal and so is at 90- 40= 50 degrees to the vertical. That's where they get the angle at the top of the triangle. Of course, the angles in any triangle add to 180 degrees so the third angle in the triangle is 180- 60- 50= 70 degrees, the last angle in the triangle.
 


They just translated the force vectors a bit, they drew the Ta force vector at the end of the downward force vector and the Tb force vector at the end of the Ta force vector.

Because the Ta vector makes an angle of 30deg with the horizontal it makes an angel of 90-30=60deg with the vertical. A similar arguments gives the angle of Tb with the vertical
 


Oooh. So I guess that these are "free vectors".

EDIT: From Gerbens reply I'll take it as a yes, since they can be moved around.
Thanks guys.
 


A vector is a thing that has only length and direction, nothing else.
 


riddle said:
Oooh. So I guess that these are "free vectors".

EDIT: From Gerbens reply I'll take it as a yes, since they can be moved around.
Thanks guys.
That is true of all vectors.
 

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